I'm in favor of radical curtailment of the burning of all fossil fuels. Anything short of that is going to be catastrophic. Yes, I know this is a pipe dream at this point. But a boy can still dream.
Deciding whether or not to burn this methane is kind of like being adrift on the north Atlantic and deciding whether or not to burn the ship to stay warm.
I think you are underestimating how much methane there is under there.
>"There is a huge amount of carbon stored in permafrost. Right now, the Earth's atmosphere contains about 850 gigatons of carbon. (A gigaton is one billion tons—about the weight of one hundred thousand school buses). We estimate that there are about 1,400 gigatons of carbon frozen in permafrost."https://nsidc.org/cryosphere/frozenground/methane.html
The beavers are going to do their thing and create comfortable habitats for themselves, which is melting the permafrost. So it looks like this gas is coming out one way or the other.
But it naturally decomposes into CO2 in a few years once in the atmosphere, so the net effect is more or less the same.
The GP is right: it would be much better if the methane just stays where it is.